numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/csyt01_rook.f | 6102B | -rw-r--r-- |
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*> \brief \b CSYT01_ROOK * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, LDC, * RWORK, RESID ) * * .. Scalar Arguments .. * CHARACTER UPLO * INTEGER LDA, LDAFAC, LDC, N * REAL RESID * .. * .. Array Arguments .. * INTEGER IPIV( * ) * REAL RWORK( * ) * COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CSYT01_ROOK reconstructs a complex symmetric indefinite matrix A from its *> block L*D*L' or U*D*U' factorization and computes the residual *> norm( C - A ) / ( N * norm(A) * EPS ), *> where C is the reconstructed matrix, EPS is the machine epsilon, *> L' is the transpose of L, and U' is the transpose of U. *> \endverbatim * * Arguments: * ========== * *> \param[in] UPLO *> \verbatim *> UPLO is CHARACTER*1 *> Specifies whether the upper or lower triangular part of the *> complex symmetric matrix A is stored: *> = 'U': Upper triangular *> = 'L': Lower triangular *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows and columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The original complex symmetric matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(1,N) *> \endverbatim *> *> \param[in] AFAC *> \verbatim *> AFAC is COMPLEX array, dimension (LDAFAC,N) *> The factored form of the matrix A. AFAC contains the block *> diagonal matrix D and the multipliers used to obtain the *> factor L or U from the block L*D*L' or U*D*U' factorization *> as computed by CSYTRF_ROOK. *> \endverbatim *> *> \param[in] LDAFAC *> \verbatim *> LDAFAC is INTEGER *> The leading dimension of the array AFAC. LDAFAC >= max(1,N). *> \endverbatim *> *> \param[in] IPIV *> \verbatim *> IPIV is INTEGER array, dimension (N) *> The pivot indices from CSYTRF_ROOK. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is COMPLEX array, dimension (LDC,N) *> \endverbatim *> *> \param[in] LDC *> \verbatim *> LDC is INTEGER *> The leading dimension of the array C. LDC >= max(1,N). *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is REAL array, dimension (N) *> \endverbatim *> *> \param[out] RESID *> \verbatim *> RESID is REAL *> If UPLO = 'L', norm(L*D*L' - A) / ( N * norm(A) * EPS ) *> If UPLO = 'U', norm(U*D*U' - A) / ( N * norm(A) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDAFAC, IPIV, C, $ LDC, RWORK, RESID ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. CHARACTER UPLO INTEGER LDA, LDAFAC, LDC, N REAL RESID * .. * .. Array Arguments .. INTEGER IPIV( * ) REAL RWORK( * ) COMPLEX A( LDA, * ), AFAC( LDAFAC, * ), C( LDC, * ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) COMPLEX CZERO, CONE PARAMETER ( CZERO = ( 0.0E+0, 0.0E+0 ), $ CONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, INFO, J REAL ANORM, EPS * .. * .. External Functions .. LOGICAL LSAME REAL CLANSY, SLAMCH EXTERNAL LSAME, CLANSY, SLAMCH * .. * .. External Subroutines .. EXTERNAL CLASET, CLAVSY_ROOK * .. * .. Intrinsic Functions .. INTRINSIC REAL * .. * .. Executable Statements .. * * Quick exit if N = 0. * IF( N.LE.0 ) THEN RESID = ZERO RETURN END IF * * Determine EPS and the norm of A. * EPS = SLAMCH( 'Epsilon' ) ANORM = CLANSY( '1', UPLO, N, A, LDA, RWORK ) * * Initialize C to the identity matrix. * CALL CLASET( 'Full', N, N, CZERO, CONE, C, LDC ) * * Call CLAVSY_ROOK to form the product D * U' (or D * L' ). * CALL CLAVSY_ROOK( UPLO, 'Transpose', 'Non-unit', N, N, AFAC, $ LDAFAC, IPIV, C, LDC, INFO ) * * Call CLAVSY_ROOK again to multiply by U (or L ). * CALL CLAVSY_ROOK( UPLO, 'No transpose', 'Unit', N, N, AFAC, $ LDAFAC, IPIV, C, LDC, INFO ) * * Compute the difference C - A . * IF( LSAME( UPLO, 'U' ) ) THEN DO 20 J = 1, N DO 10 I = 1, J C( I, J ) = C( I, J ) - A( I, J ) 10 CONTINUE 20 CONTINUE ELSE DO 40 J = 1, N DO 30 I = J, N C( I, J ) = C( I, J ) - A( I, J ) 30 CONTINUE 40 CONTINUE END IF * * Compute norm( C - A ) / ( N * norm(A) * EPS ) * RESID = CLANSY( '1', UPLO, N, C, LDC, RWORK ) * IF( ANORM.LE.ZERO ) THEN IF( RESID.NE.ZERO ) $ RESID = ONE / EPS ELSE RESID = ( ( RESID/REAL( N ) )/ANORM ) / EPS END IF * RETURN * * End of CSYT01_ROOK * END